motion comparison and recognition using microsoft kinect.pdf

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MOTION COMPARISON AND RECOGNITION USINGMICROSOFT KINECT

NOPAKORN GANJANASINIT

NOPPORN KITTIPRASERT

BACHELOR OF ENGINEERING PROGRAM IN SOFTWARE ENGINEERING

INTERNATIONAL COLLEGE

KING MONGKUTS INSTITUTE OF TECHNOLOGY LADKRABANG

2013


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ThesisAcademic Year 2013

B.Eng. in Software Engineering

International College

King Mongkuts Institute of Technology Ladkrabang

Title: Motion Comparison and Recognition using Microsoft Kinect

Authors:

1. Mr. Nopakorn Ganjanasinit Student ID : 53090016

2.

Mr. Nopporn Kittiprasert Student ID : 53090017

Approved for submission

................................................................

(Dr.Natthapong Jungteerapanich)

Advisor

Date .......................................

................................................................

(Dr.Ukrit Watchareeruetai)

Co-advisor

Date .......................................
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III

Motion Comparison and Recognition

using Microsoft Kinect

Mr. Nopakorn Ganjanasinit 53090016

Mr. Nopporn Kittiprasert 53090017

Dr.Natthapong Jungteerapanich Advisor

Dr. Ukrit Watchareeruetai Co- Advisor

Academic Year 2013

ABSTRACT

In this project, we studied and developed techniques for the similarity comparison and

the recognition of human motion. For both problems, the users motion is captured using a

Microsoft Kinect device. The captured motion is in the form of a sequence of frames where

each frame contains the positions of important joints in the users body ata specific time in the

motion.

For the motion comparison problem, we studied and developed techniques for

measuring the similarity of two given motions. The objective is to calculate the similarity of

the two motions. For this problem, we applied dynamic programming algorithms for solving

the longest common subsequence problem and the sequence alignment problem.

For the motion recognition problem, we studied and developed techniques for

recognizing which type of motions the user is performing. We focused on recognizing basic

movements in Taekwondo and applied the hidden Markov model technique. The accuracy of

experimentation as two masters and one untrained performed is 100%, 79%, and 32.5%

respectively.

For both problems, experiments were conducted to evaluate the effectiveness of the

implemented techniques. A software application supporting the capturing of motion and

experiments has also been developed using Microsoft .NET framework and Microsoft Kinect

SDK.
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IV

Acknowledgements

We would like to sincerely thank Dr. Natthapong Jungteerapanich and Dr. Ukrit

Watchareeruetai, who made it possible for us to complete this project. They always dedicated

their time for discussions about our problems throughout the project. Plus, we would like to

acknowledge with appreciations all staff members at the International College who gave

permission for us to work in the laboratory outside of office hours. Lastly, many thanks to all

our friends who always supported and inspired us to finish this project.

Nopakorn Ganjanasinit and Nopporn Kittiprasert
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V

Contents

Introduction............................................................................................................ 1

Motivation .................................................................................................................. 1

Problem Description .................................................................................................. 1

Objectives .................................................................................................................. 1

Scope of work ............................................................................................................ 2

Review of related work .............................................................................................. 2

Background Knowledge ........................................................................................ 4

Microsoft Kinect ........................................................................................................ 4

Longest Common Subsequence Problem .................................................................. 6

Sequence Alignment Algorithm................................................................................. 8

2.3.1 How two sequences are matched ................................................................ ........................ 8

Hidden Markov Model ............................................................................................. 10

2.4.1 Markov Process .......................................................... ...................................................... 10

2.4.2 Hidden Markov Model ........................................................... ........................................... 11

2.4.3 Evaluation Problem ............................................................... ........................................... 13

2.4.4 Learning Problem ....................................................... ...................................................... 16

Requirements and Software Design ................................................................... 21

Requirements ........................................................................................................... 21

3.1.1 Requirement for Motion Comparison .......................................................... ..................... 21

3.1.2 Requirement for Motion Recognition ............................................................................... 21

Use Case Diagram .................................................................................................... 21

System Architecture ................................................................................................. 22

Class Diagram .......................................................................................................... 23

Development ......................................................................................................... 24

Methodology ............................................................................................................ 24

4.1.1 Comparison of Postures ................................................................................................... 24

4.1.2 Comparison of Motion ........................................................... ........................................... 26

4.1.3 Learning HMM from motion samples .......................................................... ..................... 41

4.1.4 Classification of the Motion ....................................... ...................................................... 42

Tools and other resources used in the project .......................................................... 42

4.2.1 Kinect Device .............................................................................................. ..................... 42

4.2.2 Microsoft Visual Studio ......................................................... ........................................... 424.2.3 Kinect SDK ................................................................. ...................................................... 43


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VI

4.2.4 Microsoft XNA Game Studio ............................................................................................ 43

4.2.5 WPF ....................................................... ................................................................. .......... 43

Experimentation .................................................................................................. 44

Experiment 1: Motion comparison using sequence alignment algorithm ................ 445.1.1 Objectives ......................................................... .............................................................. .. 44

5.1.2 Procedure ......................................................... .............................................................. .. 44

5.1.3 Result ................................................................ ................................................................ 44

5.1.4 Discussion .................................................................. ...................................................... 45

Experiment 2: Effect of speed in motion comparison .............................................. 45

5.2.1 Objectives ......................................................... .............................................................. .. 45

5.2.2 Procedure ......................................................... .............................................................. .. 45

5.2.3 Result ................................................................ ................................................................ 46

5.2.4 Discussion .................................................................. ...................................................... 46

Experiment 3: Effect of position in motion comparison .......................................... 46

5.3.1 Objectives ......................................................... .............................................................. .. 46

5.3.2 Procedure ......................................................... .............................................................. .. 46

5.3.3 Result ................................................................ ................................................................ 47

5.3.4 Discussion .................................................................. ...................................................... 47

Experiment 4: Motion Recognition.......................................................................... 47

5.4.1 Objective ........................................................... .............................................................. .. 47

5.4.2 Procedure ......................................................... .............................................................. .. 475.4.3 Result ................................................................ ................................................................ 47

5.4.4 Discussion .................................................................. ...................................................... 48

Conclusion ............................................................................................................ 49

Summary .................................................................................................................. 49

Problems and obstacles ............................................................................................ 50

Future Work ............................................................................................................. 50

Bibliography ........................................................................................................................... 51

Appendix A Class Diagram ................................................................................................... 52


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VII

List of Figures

Figure Page

Figure 2.1 Microsoft Kinect ...................................................................................................... 4

Figure 2.2 The 20 joints in the users body which are tracked by Kinect ................................. 5

Figure 2.3 Source code for drawing a skeleton figure of each person tracked by Kinect .......... 6

Figure 2.4 Code for computing the table of c[i,j] values .......................................................... 7

Figure 2.5 Function for finding an LCS from the table of c[i,j] values .................................... 8

Figure 2.6 All possible transitions between state of the weather ............................................. 11

Figure 2.7 The illustration of a hermit locked up with the seaweed ....................................... 11

Figure 2.8 How the observable states can be related to the hidden states............................... 12

Figure 2.9 The observations with the possible hidden states .................................................. 13

Figure 2.10 The computation of the forward variable ........................................................... 15

Figure 2.11 The computation of the backward algorithm ...................................................... 16

Figure 2.12 The parameter estimation for complete data for a coin experiment .................... 17

Figure 2.13 The parameter estimation for complete data for a coin experiment .................... 18

Figure 2.14 The event of being at state Sat time t and state Sat time t+1 ............................ 19Figure 3.1 Use case diagram of the software .......................................................................... 21

Figure 3.2 The system architecture ......................................................................................... 22

Figure 3.3 Class diagram of the system .................................................................................. 23

Figure 4.1 How two postures are compared by absolute position .......................................... 24

Figure 4.2 How two postures are compared by angular position ............................................. 25

Figure 4.3 The code for angular measurement ........................................................................ 26

Figure 4.4 Examples of unsynchronized motion .................................................................... 26

Figure 4.5 How two motions are matched using LCS algorithm ............................................ 27

Figure 4.6 Code of sequence alignment applying for comparing motion ............................... 28

Figure 4.7 Example code for comparing three consecutive joints ........................................... 29

Figure 4.8 How feature extraction works in transforming motion to a sequence .................... 31

Figure 4.9 AR1: Right arm is above your head and is in front of your body........................... 31

Figure 4.10 AR2: Right arm is between your body and is in front of your body. ................... 32

Figure 4.11 AR3: Right arm is between your body and is at the side of your body. ............... 32

Figure 4.12 AR4: Right arm is below your body and is in front of your body. ....................... 32

Figure 4.13 AR5: Right arm is below your body and is at the side of your body.................... 33

Figure 4.14 AL1: Left arm is above your head and is in front of your body. .......................... 33

Figure 4.15 AL2: Left arm is between your body and is in front of your body. ...................... 33


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Figure 4.16 AL3: Left arm is between your body and is at the side of your body. ................. 34

Figure 4.17 AL4: Left arm is below your body and is in front of your body. ......................... 34

Figure 4.18 AL5: Left arm is below your body and is at the side of your body. ..................... 34

Figure 4.19 ER3: The angle of right arm is very small. ........................................................... 35

Figure 4.20 ER2: The angle of right arm is correct for blocking in Taekwondo. .................... 35

Figure 4.21 ER1: The angle of right arm is very wide. ........................................................... 35

Figure 4.22 ER0: The angle of right arm is too wide and it can be said you your right arm is

straight. .................................................................................................................................... 36

Figure 4.23 EL3: The angle of left arm is very small. ............................................................. 36

Figure 4.24 EL2: The angle of left arm is correct for blocking in Taekwondo. ...................... 37

Figure 4.25 EL1: The angle of left arm is very wide. .............................................................. 37

Figure 4.26 ER0: The angle of left arm is too wide and it can be said you your right arm is

straight. .................................................................................................................................... 37

Figure 4.27 L1: Both feet are at the same level and straight.................................................... 38

Figure 4.28 L2: Left foot is in front of your body and is straight. ........................................... 38

Figure 4.29 L3: Right foot is in front of your body and is straight. ......................................... 38

Figure 4.30 L4: Put left knee in front of body at around hips and kick out straightly. ............ 39

Figure 4.31 L5: Put left knee in front of your body around hips while bend your body and

kick out. ................................................................................................................................... 39

Figure 4.32 L6: Put right knee in front of body at around hips and kick out straightly. .......... 40

Figure 4.33 L7: Put left knee in front of your body around hips while bend your body and

kick out. ................................................................................................................................... 40

Figure 4.34 The example of a frame of motion to vector ........................................................ 41

Figure 4.35 The process of learning........................................................................................ 41

Figure 4.36 The process of classification of motions ............................................................. 42


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Introduction

Motivation

To determine whether the users posture is correct is straightforward. Yet, to determine

whether the users motion is correct is non-trivial. This motivated us to research on the

development of an application which can determine the correctness of the users motion as well

as provide guidance to help them making correct motions. However, due to the complexity of

this problem and the limited time available, we decide to focus on two simpler problems,namely, the motion comparison problem and the motion recognition problem. We believe that

the techniques developed for these two problems would be useful in the development of the

application which can help training the user to perform correct motions.

Problem Description

Motion comparison problem:This problem involves measuring the similarity of two

given motions. In this project, to solve this problem, we applied dynamic programming

algorithms for solving the longest common subsequence problem and the sequence alignment

problem.

Motion recognition problem: This problem involves the recognition of the type of

motions that the user is performing. In this project, we focused on recognizing basic Taekwondo

movements by applying the hidden Markov model technique.

Objectives

The main objectives of our project are as follows:

To study, develop, and test effective techniques for comparing the similarity of two

motions of a 3D human skeleton model.

To study, apply, and test hidden Markov models on motion recognition, specifically

for recognition of basic movements in Taekwondo, and analyze their effectiveness


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Scope of work

We can summarize the scope of work of our project as follows:

Study dynamic programming algorithms for solving the longest common subsequence

problem and sequence alignment problem and apply the algorithms for comparing the

similarity of motions.

Study hidden Markov model technique and apply it to recognize the users motion.

Conduct experiments to evaluate the effectiveness of the chosen techniques.

Develop an application to support motion capturing using Kinect device and facilitate

the experimentation.

Review of related work

A Motion Classifier for Microsoft Kinect [1] by Chitphon Waithayanon and

Chatchawit Aporntewan, Chulalongkorn University, describes a study of a motion classifier

based on the dynamic time warping algorithm. The authors also summarize the result of an

experiment to evaluate the accuracy of their motion classifier. Our application of the sequence

alignment technique in our project is very similar to the dynamic time warping algorithm

presented in this paper.

On-Line Handwriting Recognition Using Hidden Markov Models[6] by Han Shu,

Massachusetts Institute of Technology, describes a system for recognizing on-line cursivehandwriting in real time. The author employs hidden Markov models to model handwritten

characters, words, and sentences. The paper also describes a technique for selecting appropriate

features to be used as observables states in hidden Markov models. We learned the basics of

hidden Markov models and their application from this paper and applied them for our work on

motion recognition.

DNA Sequence Alignment using Dynamic Programming Algorithm[8], by Sara

El-Sayed El-Metwally, introduces the basic idea of sequence alignment algorithm and applies

the algorithm for DNA analysis. In this work, the author shows how two DNAs are matched by

applying an algorithm for sequence alignment. The algorithm explained is based on the

dynamic programming technique.

Kinect Based Dynamic Hand Gesture Recognition Algorithm Research [9], by

Youwen Wang, Cheng Yang, Xiaoyu Wu, Shengmaiao Xu, and Hui Li, Communication

University of China, tries to solve the problem of hand gesture recognition. The technique

described in the paper focuses on the position of the userspalms and employs hidden Markov

models. The paper also summarizes the result of an experiment to assess the recognition


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accuracy. Moreover, the authors present an interesting feature extraction technique, which we

adapted for use in our project.


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Background Knowledge

Microsoft Kinect

Microsoft Kinect is a device in Microsoft Xbox gaming platform. It has been developed

by Microsoft since the beginning of November 2010. Within a Kinect device, there are several

cameras attached to enable the user to control and interact with the game or software application

without the need of a game controller. The application receives the users input through users

gestures or spoken commands.

A Kinect device consists of three main components. The first component is an RGB video

camera which captures color videos. The second part is a 3D depth Sensors which uses infrared

projection to measure the distance of objects from the device. The last part is an array of four

microphones, which is used to receive spoken commands from multiple users at the same time.

Figure 2.1 Microsoft Kinect

Kinect (in conjunction with the Kinect for Windows SDK software) utilizes its video

camera and depth sensor to track the people within its field of view. Kinect can report the

positions of up to 6 people simultaneously in real time (30 frames per second). Moreover, two

people located at the optimal distance from the device will be marked as active. Kinect does

not only report the positions of the active persons, but also performs feature extraction to locate

the important joints within each of the active persons. Figure 2.2 depicts the 20 important joints

which are tracked by Kinect. [2]


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will call the method called DrawSkeletonPosition, which only draws a jointless skeleton

figure for that person.

void sensor_SkeletonFrameReady(object sender,

SkeletonFrameReadyEventArgs e)

{

Skeleton[] skeletons = new Skeleton[1];

using (SkeletonFrame skeletonframe = e.OpenSkeletonFrame())

{

if (skeletonframe != null)

{

skeletons = new Skeleton[skeletonframe.SkeletonArrayLength];

skeletonframe.CopySkeletonDataTo(skeletons);

foreach (Skeleton skeleton in this.skeletonData)

{

if (skeleton.TrackingState == SkeletonTrackingState.Tracked)

DrawSkeletonJoints(skeleton);

else if (skeleton.TrackingState ==

SkeletonTrackingState.PositionOnly)

DrawSkeletonPosition(skeleton);

}

}

}

}

Longest Common Subsequence Problem

The longest common subsequence problem is a classic problem in computer science. It

has many applications in various fields, including in DNA analysis. Given a sequence X =

, a subsequenceof X is any (possibly empty) sequence ofelements in X such that

1 < < < . Given two sequences X =

and Y = , a common subsequenceof X and Y is any sequencewhich is a subsequence of both X and Y. Then the longest common subsequence problem asks

for a longest common subsequence (LCS) of two given sequences X and Y.

Lets look at an example. Consider the following sequences

X =

Y =

An LCS of these two sequences is .

Figure 2.3 Source code for drawing a skeleton figure of each person tracked by Kinect


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A well-known algorithm [10] for solving the longest common subsequence problem

employs the dynamic programming technique. Essentially, the algorithm proceeds by

computing the length of a longest common subsequence of the given sequences. Precisely,

suppose the given sequences are X = and Y = . Let

[,],

where 0 and 0 , denote the length of a longest common sequence of thesequences and . It is quite clear that [,]satisfies the followingequations:

[, ] 0 if 0 or 0[ 1 , 1] 1 if , > 0 and ([, 1],[ 1, ]) if , > 0 and To find [,] by dynamic programming, we construct a table of size (m+1) (n+1)

and compute the value of [,], for each and, starting from 0and 0until and j =n, using the above equations, and fill the value of [,]in the cell at row and column. After filling in the table, the value in the cell at row and column will contain the lengthof a longest common subsequence ofand .

Figure 2.4 contains a sample code fragment for computing the table of [,]as describedabove.

Figure 2.4 Code for computing the table of c[i,j] values

Once we have the table of [,], we can read out a longest common subsequence of and from the table by computing the sequence (,)recursively as follows:

(,)empty string if 0 or 0( 1 , 1) if , > 0 and ( 1 , ) if , > 0 and c[ 1 , ] [ , 1 ]( , 1) if , > 0 and c[ , 1] > [ 1 , ]

c = array(0..m, 0..n)

for i := 0..mc[i,0] = 0

for j := 0..nc[0,j] = 0

for i := 1..mfor j := 1..n

if X[i] = Y[j]c[i,j] := c[i-1,j-1] + 1

elsec[i,j] := max(c[i,j-1], c[i-1,j])


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where + denotes sequence concatenation. Figure 2.5 contains a sample code of a function for

finding a longest common subsequence ofand from the table of [,]. The function shouldbe called with the argument and .

Figure 2.5 Function for finding an LCS from the table of c[i,j] values

Sequence Alignment Algorithm

It is a technique for comparing two or more sequences by looking for a series of

characters that are in the same order in all sequences. Two sequences will be matched in

systematic way: identical or similar characters will be matched together, and non-identical ones

will be matched either as mismatch or putting a gap (-). This algorithm is considered to be

useful to do the biological sequences. The example show how two string sequences are

matched. The two strings are GAATTCAGTTA and GGATCGA.

String1: G _ A A T T C A G T T A| | | | | |

String2: G G _ A _ T C _ G _ _ A

2.3.1 How two sequences are matched

Sequence Alignment algorithm uses matrix for matching two subsequences. It is a

matrix in the size of . (X = length of the first sequence, Y= length of the secondsequence) with initializing the first row and column with the gap penalty equals to I Gap.

For example, we have two sequences: (10, 10, 20, 30, 30, 40) and (10, 20, 20, 30, 40,

40) with gap penalty (G) = 5 and mismatch penalty (D) = 1, so now we have the matrix shown

below.

function findLCS(i, j)if i = 0 or j = 0

return ""else if X[i] = Y[j]

return findLCS(i-1, j-1) + X[i]else

if c[i,j-1] > c[i-1,j]return findLCS(i, j-1)

elsereturn findLCS(i-1, j)


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Therefore, we traverse back from [5,5]back to [1,1]according to thearrow. The result will be just like what they are matched and the total difference cost is the last

matrix cell which is 20. The direction of arrows is indicated as follows:

= match both Sequence 1 and 2

= match Sequence1 with gap

= match Sequence2 with gap

Two sequences are matched as follows:

Sequence1: 10 10 20 30 30 40| | | | | | | |

Sequence2: 10 20 20 30 40 40

Hidden Markov Model

When the user distorted the gesture of model, the program is supposed to correct by

suggesting. In the easy way, we could say something like The user should put right foot up 13

cm. at the third second. However, this sentence is not so meaningful. Instead we could say

The user should do the kick of right legs at the third second.

To do so, we need our program to be able to tell the motion. Therefore, we need to do

the motion recognition to know what motion the user is doing.

2.4.1 Markov Process

A Markov process is a process which moves from one state to the next sate depending

only on previous state. The figure below shows that transitions between states of weather. Each

transition has its state transition probability. It is the probability of a state moving to another.

For example, the possibility of todays weather, sunny, to tomorrows weather, raining, is 0.34.

The important assumption about the process is that state transition probabilities are independent

of the actual time.


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Suppose the hermit observe the following sequence of seaweed dampness in a week:

Soggy, Damp, Damp, DryishWhat is the most likely pattern of weather?

From the problem, we come up with the solution of using Hidden Markov model so the

hermit can tell the weather by noticing the dampness of seaweed. Hidden Markov model is a

stochastic method to find patterns of sequence data. In Hidden Markov model, the hidden states

are related to the observable states somehow. So we can model the processes as in the figure

2.8.

Furthermore, in order to do the Hidden Markov model, we need three groups of

parameters defined:

= ( ) Matrix of initial probabilities, describing the probabilities of eachhidden state being in the first state.

A = ( a ) Matrix of state transition of probabilities, describing the probabilitiesof state i moving to state j.

B = ( b ) Matrix of observation probabilities, describing the probabilities ofobservable state j at specific hidden state i.

Figure 2.8 How the observable states can be related to the hidden states2

Therefore, a hidden Markov model is a standard Markov process combined with a set

of observable states and some probabilistic relations between them and the hidden states.

2

source: http://www.comp.leeds.ac.uk/roger/HiddenMarkovModels


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There are three fundamental problems of hidden Markov models

Evaluation: To calculate the probability of the observation sequence given the model.

Decoding: Given the observation sequence and model, we can find the optimal state

sequence.

Learning: Given the observation sequences, find the parameters of the HMM which

generates those observation sequences with highest probabilities.

Well-known algorithms for solving Evaluation, Decoding, and Learning are Forward

algorithm, Viberti algorithm, and Baum-Welch algorithm respectively.

2.4.3 Evaluation Problem

Given the observation sequence O =

, and a model = (,A,B), how do

we efficiently compute P(O| ), the probability of the observation sequence, given the model?

[7]

Figure 2.9 The observations with the possible hidden states3

Suppose we observed the dampness of seaweed for three consecutive days which are

dry, damp, soggy given the HMM and we want to know the probability of this observation

sequence.

The exhaustive way to do this is to find all possible sequence of hidden states and sum

them all together. For the above example, we will get the probability as

(,,|) (, , | , , ) (, , | , ,)

3

Source: http://www.comp.leeds.ac.uk/roger/HiddenMarkovModels


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(, , | , , ) . . . .

(, , | , , )

It can be seen that this is computationally expensive. Fortunately, forward algorithm

exists to solve this problem much efficiently.

The forward algorithm has some variable to be considered which is ()defined as()= (, = | )

This means the probability of the partial observation sequence at time = 1 to time = t

and being at state at time t given the model . We can solve for this problem as follows [7]:1)

Initialization:()= (), 1 2) Induction:+()= [ ()= ](+), 1 1 , 1 3) Termination(| )= ()= In the Initialization case where t = 1, since there are no paths coming to the state, the

initial probability is

( | 1)

()in the Matrix of initial probabilities and

we then calculate this partial probabilities by multiplying with the associated observation. To

put it simply, the probability at the first state is equal to the states probability together with the

probability of that specific observation at the time.


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Figure 2.10 The computation of the forward variable [7]

In the Induction case where t >1, this is the essential part to make the forward

calculation shown in figure 2.10(a). This figure shows how we can reach state

at time t+1

from every possible state, ,,,. Since ()is the probability of and is atthe state at time t, therefore, () is the probability of and is at the state attime 1. By adding up this product from all the possible states, ,,,, at time t, wewill get the possibility of at time t+1. Once we know , +()can be calculated easily bymultiplying this added up quantity with (+). From the Inductive formula, it is the result ofall states at a given time (1,2,,1).

Last case, Terminal, gives us the desired result of

(| ). It is the summation of

probabilities as().Evaluation problem is used to compute the probability that the model can produce the

observed sequence. The probability is like the score, we can see how well the observed

sequence fit with the model. To solve this problem is certainly useful for us to do the motion

recognition. Imagine that we have the models according to each Taekwondo movement, this

helps us to choose the best Taekwondo movement model which best matches with the observed

sequence.


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In Evaluation problem, the forward is actually needed. However, backward algorithm

which works in similar way to the forward algorithm also needed for learning problem.

Therefore, it will be explained here.

Backward algorithm works in the similar manner as forward algorithm. Yet, as the

name said, it works from the back. Therefore, the formula of the backward algorithm [7] is

()= P(++ |= , )This is the probability of the partial observed sequence from time t+1 to the end given

that being in the state at time t and model . We can solve for this problem as follows [7]:1) Initialization:()= 1, 1 2)

Induction()= = (+)+(), 1, 2, ,1 , 1 In Initialization case, (i) is freely defined to be 1 for every i.In Induction case, it can be seen that being in state at time t, all path from 1

on has to be considered. To put it simply, all possible transitions from at time t+1 to areconsidered by multiplying with (+) and +() which is the remaining partialobserved sequence. Later, this algorithm will be used with forward algorithm to help solving

learning problem.

Figure 2.11 The computation of the backward algorithm [7]

2.4.4 Learning Problem

In learning problem Baum-Welch algorithm is applied. It uses the concept of

expectation maximization so getting to know expectation maximization first will, of course,

help you get a better and deeper understanding of Baum-Welch algorithm.

Expectation Maximization is a method to find the maximum likelihood. It will be very

useful when some of your parameters are unobserved. It tries to guess these parameters and


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then reestimate the model parameter which will be the new actual likelihood. It continues

calculating until convergence.

Figure 2.12 The parameter estimation for complete data for a coin experiment[11]

Letstake a simple example of a coin-flipping experiment with complete set.

Suppose that we have two coins A and B which are unknown whether they are fair or

not and suppose that is the probability of coin A lands on head and 1-is the probabilityof coin A lands on tail. Same apply to coin B. In the experiment, we randomly pick the coin A

or B and toss it for ten times. Repeatedly do this for five times as shown in figure3.9. In the

experiment, two vectors, x = (x,x, , x) and z = (z,z, , z), are observed. Vector x is forkeeping track of the number of heads happening at that iteration. Vector z is for keeping track

of which coin is tossed during that iteration.

After the experiment is conducted, the way to estimate and is= # # and

=

# #

Since all data are complete, this is known as maximum likelihood which is of the

statistical model based on the probability.


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Figure 2.13 The parameter estimation for complete data for a coin experiment[11]

However, in Expectation Maximization, the data is not complete. For example in the

coin-flipping experiment, the vector x is given, but the vector z is not. This means we dont

know which coin used in each iteration. Therefore, guessing which coin was used in each timeis a good option to complete the data.

The Expectation Maximization algorithm, firstly, guess the value for model parameters

= (,). Then, it will do two big steps: E-step and M-step. After guessing, it starts with theE-step, it will determine using the current parameter to estimate whether coin A or coin B is

more likely to produce the observed flips. Then in M-step, it will apply the maximum likelihood

to get a new . Repeatedly do this two steps until convergence. This algorithm confirms the

improvement of the model parameter. This process can be seen in the figure 2.13 (b).

Now, we have enough understanding of expectation maximization we can go for the

Baum-Welch method for the learning problem. The heart of learning problem is

How do we adjust the model parameters (,,)to maximize (| ) [7]Baum-Welch algorithm takes care of the part quite efficiently by iteratively

reestimating and improving the HMM parameters. Firstly, (,) is introduced. It is theprobability of being at state Sat time t and state Sat time 1, given the model and observedsequence. This can be written in the formula as:

(,) (q S, q+= S| ,)


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Figure 2.14 The event of being at state at time t and state at time t+1[7]According to the figure 2.14, it is quite clear that it is the combination of the forward

algorithm with the backward algorithm. The part of being at state Sat time t requires theforward algorithm and the part of being at state Sat time t and state Sat time t+1 requiresbackward algorithm. Together, we can write (,)in the new form[7]:

(,)= ()()()(| ) = ()()() ()()()

From the formula, the numerator is (q S, q+= S | ,)and we need to divideby (| ),which is the probability of the whole observed sequence given the model, to givesus the desired probability measure.

Now,(i) will be introduced. It is the probability of being in state Sat time t, giventhe model and observed sequence. It is said that ()is related to (,)by adding over j,therefore

()= (i,j)= , [7]Now, lets take another consideration. If()is added over the time index , we will

get a number which is the time of state Sbeing visited or the number of Smakes the transition.Similarly, the addition of (i,j)over the time index is the number of transitions from Sto S.

This consideration helps us to reestimate the parameter of HMM (, A, and B). Wereasonably reestimate as follow [7]:

= the number of times being at state Sat time t=1


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= () =

= (,) () b =

=

() () After reestimating and update the parameter, Baum-welch algorithm makes sure to

improve the likelihood of the given sequences produced.

Learning problem is used to adjust the parameter in the model. In this case, the observed

sequences are used as training set. The more observed sequence for training the model, the

better accurate we get when we do the evaluation. After the model is trained, the model is said

to describe that specific gesture movement. In our project, we have the Hidden Markov models

for each Taekwondo movement. Then 15 samples are performed as a training set for each

Hidden Markov model. At the end, we have Hidden Markov models suit for each Taekwondo

movement. Afterward, HMMs are used in Evaluation problem.


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Requirements and Software Design

Requirements

3.1.1 Requirement for Motion Comparison

The system efficiently calculates the similarity of two motions and gives result in

number. The less you get a score, the better you performed.

The system allows a user to record his/her motion.

The system can save and replay recorded motions.

3.1.2 Requirement for Motion Recognition

The system is able to determine what Taekwondo gesture he/she is doing.

The system is able to learn the Taekwondo gesture file from user

The system allows a user to record his/her motion.

The system can save and replay recorded motions.

Use Case Diagram

Figure 3.1 Use case diagram of the software


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System Architecture

First of all, the user got all the samples of all gesture movements. The user has to let the

program learn all the samples accorded to each gesture movement. When it is done, the program

would know how each gesture movement is like.

To do the recognition of motion, a user stands in front of the Kinect device. When the

user moves or do any gestures, he/she will see their movement by using Kinect SDK in our

application and display on the screen. By using this Kinect SDK, it provides us many

functionalities to implement the code for recognition. However, in order to do the Taekwondo

recognition, he/she does any Taekwondo gestures and the program will tell what the gesture

he/she is doing. Similarly, to do the motion comparison, the user pick the model he/she wants

to perform. Then, when user starts moving accordingly to the model, and at the end, the program

will compare and finally, show the result of similarity in number.

The program is also connected to the database and is able to add the name of gesture and

record the samples of each gesture. The database then stored all those name.

Figure 3.2 The system architecture


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Development

Methodology

4.1.1 Comparison of Postures

4.1.1.1 Absolute Posit ion M easurement

This method compares the absolute position of each joint of the user with that of the

model. Kinect SDK provides us a method which can get the position X, Y, and Z. We first

straightly compare one by one joint by calculating the difference. If the value meets criteria, we

will give scores.

However, there might be a situation that user does the exact posture as models but

stand in the different position because joint positions depend on where the user stands.

To avoid requiring the user to stand at a fixed position, we measure the position of each joint

relative to the body center (called a normalized position). Yet, it is still problematic if the users

body size differs from the models body size.

Figure 4.1 shows that the X and Y position of model are different from users position,but after we normalized them both, the X and Y position of both users posture and models

posture are same.

Right hand: 0.4012965, 0.6971655 Right hand: -0.2483381, 0.6861519

Normalized position: 0.2433355, 0.5104655 Normalized position: 0.2433355, 0.5104655

Figure 4.1 How two postures are compared by absolute position

4.1.1.2 Angular Measurement

This method compares the angles between adjacent bones of the user with those of the

model. From 20 body joints the Kinect can recognizes, we calculate, by creating two vectors


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joint1Tojoint2 = newMicrosoft.Xna.Framework.Vector3(joint2.Position.X -joint1.Position.X, joint2.Position.Y - joint1.Position.Y,joint2.Position.Z - joint1.Position.Z);

joint0Tojoint1.Normalize();joint1Tojoint2.Normalize();

doubledotProduct =Microsoft.Xna.Framework.Vector3.Dot(joint0Tojoint1,joint1Tojoint2);crossProduct =Microsoft.Xna.Framework.Vector3.Cross(joint0Tojoint1,joint1Tojoint2);doublecrossProdLength = crossProduct.Length();doubleangleFormed = Math.Atan2(crossProdLength,dotProduct);doubleangleInDegree = angleFormed * (180 / Math.PI);

doubleroundedAngle = Math.Round(angleInDegree, 2);

returnroundedAngle;}

4.1.2 Comparison of Motion

A motion can be seen as a sequence of consecutive postures. But we cannot simply

compare two motions by comparing the sequences of postures directly, because the two

motions may not be perfectly synchronized. There are many factors involved here: velocity,

delay, or rhythm. For example, differing initial delays could happen when the user started one

step slower than the models model. In another case, when the user happens to do the motion

faster than the models motion, it is said to be called differing initial speeds.

Figure 4.4 Examples of unsynchronized motion

Figure 4.3 The code for angular measurement


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To solve this problem, we adopt the Longest Common Subsequence algorithm, and

Sequence Alignment algorithm.

4.1.2.1 Longest Common Subsequence Algori thm for motion

We apply LCS by first saving the models motion into a file. Then we capture the usersmotion and compare it using the LCS algorithm with that of the model.

As a result, the degree of similarity of the two motions is determined from the length of the

LCS (the longer the LCS the more similar the motions).

Figure 4.5 How two motions are matched using LCS algorithm

However, problems with the LCS technique is that in two postures which look exactly

alike, the position of each joint in one posture may slight differ from the position of that joint

in the other posture. So when comparing the positions of joints in two postures, some errors

must be allowed. Plus, the algorithm only calculates without looking at how much different the

non-common parts are. Furthermore, Computational Expensive is another problem which

happens to be (()where n is the motion length).4.1.2.2 Sequence Al ignment Algorithm for motion

How Sequence Alignment is applied for motion comparison


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Figure 4.6 Code of sequence alignment applying for comparing motion

Since the motion can be seen as a sequence of skeletons, we can do the same

algorithm by treating each frame of skeleton as a character of a string. The([],,) in the algorithm is the different value calculated from angularmeasurement of two skeletons. This different value is the number of three consecutive joints

that have the degree of angular in models skeleton and users skeleton not exceed 15 degrees.

In ([],,) function, we compare 16 times of any threeconsecutive joints as follows:

Right hand, Right wrist, Right elbow

Right wrist, Right elbow, Right shoulder

Right elbow, Right shoulder, Center shoulder

Right shoulder, Center shoulder, Head

Right shoulder, Center shoulder, Left shoulder

Center shoulder, Left shoulder, Left elbow

Head, Center shoulder, Left shoulder

Left shoulder, Left elbow, Left wrist

Left elbow, Left wrist, Left hand

Head, Center shoulder, Spine

Center hip, Right hip, Right knee

Center hip, Left hip, Left knee

Right hip, Right knee, Right Ankle

Left hip, Left knee, Left ankle

Right knee, Right ankle, Right foot

Left knee, Left ankle, Left foot


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In any consecutive joints mentioned above, we calculate the angle from the model

and from the user and then we subtract these two numbers as the code follows:

doubleHRtoWRtoERofModel = getSegmentAngle(askel, JointType.HandRight,JointType.WristRight, JointType.ElbowRight);doubleHRtoWRtoERofUser = getSegmentAngle(askel, JointType.HandRight,JointType.WristRight, JointType.ElbowRight);doublediff = Math.Abs(HRtoWRtoERofModel - HRtoWRtoERofUser);

The code explain in details that first we find the value of HRtoWRtoERofModelwhich

is the angle of the three consecutive joints of right hand, right wrist, and right elbow of model

using getSegmentAnglefunction. Then, we find the value of HRtoWRtoERofUser which is

the angle of the three consecutive joints of right hand, right wrist, and right elbow of user using

getSegmentAnglefunction. Then we obtain diff value which is the different angle of these

two frames. Then we have a threshold of 15 degrees. If the value of diff does not exceed 15,

then we say that these three consecutive joints of model and user are similar.

After you have calculated this for 16 times from list of joints mentioned above, we conclude

that the value of diff is 0 if they are completely similar. On the same hand, if the value of

diff is 16, it is said that they are completely different.

Later, we found that the value of D and G affects the result. We consider that there

might be cases where two motions are completely different.

Table 4.1 Two worst case possible in sequence alignment

Pattern Matched Pattern Condition

Sequence1: G G G G - - - -

| | | | | | | |

Sequence2: - - - - G G G G

( 1 2) Sequence1: D D D D

| | | |

Sequence2: D D D D G G ( 1, 2) ( 1 2) However, we treat these two cases to be the worst case after all. Therefore we come

up with the formula.

(1 2) 1 ( 2 1) Therefore,

2

Figure 4.7 Example code for comparing three consecutive joints


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So we conclude that in our application, we should specific the value of penalty,

mismatch (D) and Gap(G) to be accorded to the formula.

In (,) function which we calculate this value from doing angularmeasurement and normalize the value to range from zero to one which zero is said that two

postures are exactly the same and likewise, one is said that two postures are totally different.

However, in reality, it is unlikely that user will do exactly the same or totally different.

Therefore, we have to do the normalization again. If the comparison was 0.2, we would say that

user doing great as zero. Similarly, if the comparison was 0.4, we would say that user doing

quite poor. According to the formula, we said 0.2 is best and 0.4 is worst.

(, ) (1, (0, (, ) )/( ))According to the algorithm, the difference value can be taken from the last cell of

the matrix. Yet, we need to recalculate to percentage using the formula.

[,] 1 2 100This percentage will be shown as a similarity of two motions.

The good things using this algorithm are that it fixes that problem of LCS algorithm.

It allows the position of each joint in one posture may slight differ from the position of that

joint in the other posture so it does not have to be exactly alike. However, users have to pay for

a D cost. Sometimes, it puts a gap penalty to improve your matching.

4.1.2.3 Velocity Measurement f or motion

This method compares using the velocity of each joint of the user with each of those in

the model. From 20 body joints the Kinect device can recognizes, in each frame, we calculate

the velocity of each joint using the formula.

2 1 where S2-S1 = the displacement of specific joint in the next frame and this frame

Using this formula, as a result, we get the value of velocity in each frame. For further

analysis, we would use this as a way to suggest and correct users, if they happened to move

slower or faster than the models motion.


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4.1.2.4 Feature Extr action

As we have mentioned before, in HMM, some sequences has to be observed in order

to learn or evaluation. However, we cannot let each frame of the motion as a sequence. Some

feature has to be extracted out of a frame. Therefore, we are going to transform the motion to

the sequences of observations

Figure 4.8 How feature extraction works in transforming motion to a sequence

Since we are going recognize the Taekwondo movements, the feature has to be

extracted referring to the analysis of Taekwondo movements. The analysis of Taekwondo

movement is divided into five features which each one takes care of each part of body: right

arm, left arm, right elbow, left elbow, lower part of body. Therefore, one frame will be checked

according to these features and stored as a vector.

Arm-Right: The feature focuses on only right arm

Figure 4.9 AR1: Right arm is above your head and is in front of your body.


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Figure 4.10 AR2: Right arm is between your body and is in front of your body.

Figure 4.11 AR3: Right arm is between your body and is at the side of your body.

Figure 4.12 AR4: Right arm is below your body and is in front of your body.


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Figure 4.13 AR5: Right arm is below your body and is at the side of your body.

Arm-Left focuses only on left arm

Figure 4.14 AL1: Left arm is above your head and is in front of your body.

Figure 4.15 AL2: Left arm is between your body and is in front of your body.


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Figure 4.16 AL3: Left arm is between your body and is at the side of your body.

Figure 4.17 AL4: Left arm is below your body and is in front of your body.

Figure 4.18 AL5: Left arm is below your body and is at the side of your body.


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Elbow-Right focuses only the angle of right elbow

Figure 4.19 ER3: The angle of right arm is very small.

Figure 4.20 ER2: The angle of right arm is correct for blocking in Taekwondo.

Figure 4.21 ER1: The angle of right arm is very wide.


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Figure 4.22 ER0: The angle of right arm is too wide and it can be said you your right

arm is straight.

Elbow-Left focuses on the angle of left arm

Figure 4.23 EL3: The angle of left arm is very small.


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Figure 4.24 EL2: The angle of left arm is correct for blocking in Taekwondo.

Figure 4.25 EL1: The angle of left arm is very wide.

Figure 4.26 ER0: The angle of left arm is too wide and it can be said you your right arm

is straight.


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Figure 4.30 L4: Put left knee in front of body at around hips and kick out straightly.

Figure 4.31 L5: Put left knee in front of your body around hips while bend your body

and kick out.


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Figure 4.32 L6: Put right knee in front of body at around hips and kick out

straightly.

Figure 4.33 L7: Put left knee in front of your body around hips while bend your

body and kick out.


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Figure 4.34 The example of a frame of motion to vector

For example, from the picture, we got the vector (Right Arm, Left Arm, Right Elbow,

Left Elbow, Lower part of body) as (2,2,3,3,4)and this is one of our features inone motion. To put in simply, it is one observation in the observed sequence.

4.1.3 Learning HMM from motion samples

To learn in HMM, we need a training set. For example, we want a HMM for left front

kick so we perform a left front kick 15 times as 15 samples. Then we let the HMM of left front

kick learn all the samples.

Figure 4.35 The process of learning


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Experimentation

Experiment 1: Motion comparison using sequence alignment

algorithm

5.1.1 Objectives

The experiment one is conducted in order to show how two similar motions compared

give better value comparing to those two motions where two different motions compared.

5.1.2 Procedure

We prepared five different movements and in each movement, we prepare 10 samples.

The five movements we have prepared are jumping jack, jogging, stretches, waving hand, and

stretch arms while twist hip.

Therefore, for each movements i, there are 10 samples, named .1 , .2 ,, .10. Wecan create a confusion matrix of the average difference between the samples in each pair of

movements. Precisely, we define a matrix

[1,,5][1,5]as follows:

[][] (. , . ), 1 , 10, ! ,[][] (., . ), 1 , 10, ! ,[][] [][],

where i and j are the number of movement and s and t are the number of sample.

5.1.3 Result

The list of movement: 1 (Jumping Jack), 2 (jogging), 3 (stretches), 4 (waving hand), 5(stretch arms while twist hip).


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Table 5.1 The result of Experiment 1

5.1.4 Discussion

This result as a confusion matrix proves that two same motions compared give less value

than two different motions compared. In the diagonal cells of the matrix, show the small number

which mean two motions are similar.

Experiment 2: Effect of speed in motion comparison

5.2.1 Objectives

The experiment two is conducted in order to show the same motions in different speed

give the difference value.

5.2.2 Procedure

We prepared just only one movement with four samples. That one movement is the

movement of hands waving while moving up and down together in different speed starting from

slowest to the fastest.

Therefore, there are 4 samples, named 1, 2, , 4. We can create a matrix to show thedifference between each pair of samples.

4, 4,[][] 0,[][] (, ),[][] [][],

where i and j are the number of a sample.

1 2 3 4 5

1 4 31 45 27 47

2 11 48 17 50

3 7 39 32

4 6 31

5 5


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5.2.3 Result

Starting from slowest (1) to the fastest (4), we waved both hands up and down three

times in different speed. As a result, we got this matrix,

Table 5.2 The result of Experiment 2

1 2 3 4

1 0 17 39 63

2 0 23 52

3 0 33

4 0

5.2.4 Discussion

It can be seen in the diagonal cells of matrix that same samples result in zero because

they are compared with themselves. The rest of matrix cell we come up with conclusion that,

the more two motions are different in speed, the more difference value we get.

Experiment 3: Effect of position in motion comparison

5.3.1 Objectives

The experiment three is conducted in order to show how the same motions in different

position give the difference value.

5.3.2 Procedure

We prepared just only one movement with four samples. That one movement is the

movement of waving two hands in different position.

Therefore, there are 3 samples, named 1, 2, 3. We can create a matrix to show the

difference between each pair of samples.

3, 3,[][] 0,[][] (, ),[][] [][], .,


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5.3.3 Result

Table 5.3 Result of Experiment 3

1 2 3

1 0 6 10

2 0 3

3 0

5.3.4 Discussion

This experiment shows that the different positions of doing the same movement are

treated as the same motion with the comparing of angular.

Experiment 4: Motion Recognition

5.4.1 Objective

The experiment four is conducted in order to determine how accurate the system can

recognize the motion.

5.4.2 Procedure

We have 16 primitive gestures. Each one has its own 60 samples performed by two

masters. The first 40 random samples are for to learn. Another 20 random samples are for to

test.

After we let all primitive gestures learn the movement. We start to test the accuracy.

The process is to do the evaluation of each sample of each motion with the Hidden Markov

model. We will see whether the sample is correct according to the model of Hidden Markov or

not.

5.4.3 Result

Table 5.4 The experiment of motion recognition

TKD Movement Master 1 Master 2 Unskilled user

Right Front Kick 100% 90% 90%


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TKD Movement Master 1 Master 2 Unskilled user

Left From Kick 100% 70% 70%

Right Round Kick 100% 100% 90%

Left Round Kick 100% 100% 100%

Right Low Block 100% 70% 10%

Left Low Block 100% 80% 0%

Right Middle Block 100% 90% 10%

Left Middle Block 100% 90% 0%

Right Inside Block 100% 100% 0%

Left Inside Block 100% 100% 30%

Right High Block 100% 100% 20%

Left High Block 100% 100% 0%

Right Double Knife

Hand Block100% 100% 100%

Left Double Knife

Hand Block100% 80% 0%

Average 100% 79% 32.5%

5.4.4 Discussion

This experiment shows that the motion recognition is quite accurate for ones who are

skillful in Taekwondo. For those who are amateur to Taekwondo, the score could be poor

because of the lack of experience in Taekwondo.


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To support the experimentation, we implemented a program to help facilitating the

recording and organization of sample motions and automating the experiments. The program

was written in Microsoft Visual C#.

Problems and obstacles

Below are the problems and obstacles we experienced while working on this project.

The limitation of Kinect affected the kick movement in Taekwondo. When two or

more joints overlap, the accuracy of the positions of such joint reported by Kinect

can be very poor.

It was hard to conduct an experiment because we had to record the motions

ourselves.

It was hard to find a Taekwando master willing to help provide sample motions.

It is very difficult to understand the hidden Markov model technique. Extensive

knowledge in probability and statistics is required.

Future Work

In case we are continuing this project in the future, we will improve the motion

comparison algorithms in terms of speed. Also, we would like to extend our motion recognition

program, which is based the hidden Markov model technique, to be able to recognize a sequence

of Taekwando movements performed continuously by the user. As our ultimate goal, we would

like to develop a program that can provide guidance to the user when he/she does not perform

the required series of Taekwando movements correctly. We believe that such a program would

be very useful for Taekwando training and the technique developed would have applications in

other sports or activities.


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Bibliography

[1] Chitphon Waithayanon and Chatchawit Aporntewan. A Motion Classifier for Microsoft

Kinect.Chulalongkorn University.

[2] Wikipedia, the free encyclopedia, Kinect,http://en.wikipedia.org/wiki/Kinect.

[3] Rotation in 3D,

http://www.cs.science.cmu.ac.th/person/ekkarat/graphics/chapter/chapter8_2.htm

[4] Fletcher DunnIan Parberry, 3D Math Primer for Graphics and Game Development,

pp 229-232Second Edition 2011.

[5] Stack Overflow, What's a quaternion rotation?,

http://stackoverflow.com/questions/4023161/whats-a-quaternion-rotation.

[6]

Han Shu, On-Line Handwriting Recognition Using Hidden Markov Models,

Electrical Engineering and Computer Science Massachusetts Institute of Technology

(1996).

[7] LawRence R. Rabiner, A Tutorial on Hidden Markov Models and Selected

Applications in Speech Recognition, IEEE, Vol.77, No2, pp 257-265 (1989).

[8] Sara El-Sayed El-Metwally, DNA Sequence Alignment using Dynamic Programming

Algorithm, http://www.codeproject.com/Articles/304772/DNA-Sequence-Alignment-

using-Dynamic-Programming-A

[9] Youwen Wang, Cheng Yang, Xiaoyu Wu, Shengmiao Xu, Hui Li, Kinect Based

Dynamic Hand Gesture Recognition Algorithm Research, College of Information

Engineering, Communication University of China, Beijing, China (2012).

[10] Pinyo Taeprasardsit, Dynamic Programming: Principles, Applications, and

Competition, Silpakorn University (2012).

[11] Chuong B Do & Serafim Batzoglou, What is the expectation maximization

algorithm?,Primer (August 2008).


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Appendix A

Class Diagram

showswhereKinect

readyprovided

motion comparison and recognition using microsoft kinect.pdf

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